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The magnetic field due to a current-carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is 54 μT. Its value at the centre of the loop is CμT. What is the value of C?
Correct answer is '250'. Can you explain this answer?
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The magnetic field due to a current-carrying circular loop of radius ...
Given:
- Radius of the circular loop, r = 3 cm
- Distance from the center of the loop to the point on the axis, x = 4 cm
- Magnetic field at the point on the axis, B = 54 μT
To find:
- The value of the magnetic field at the center of the loop, C
Explanation:
The magnetic field due to a current-carrying circular loop at a point on its axis can be calculated using the formula:
B = μ₀ * I * R² / (2 * (R² + x²)^(3/2))
Where:
- B is the magnetic field at the point on the axis
- μ₀ is the permeability of free space, which is a constant value
- I is the current flowing through the loop
- R is the radius of the loop
- x is the distance from the center of the loop to the point on the axis
Step 1: Convert the given values to SI units:
- Radius of the circular loop, r = 3 cm = 0.03 m
- Distance from the center of the loop to the point on the axis, x = 4 cm = 0.04 m
- Magnetic field at the point on the axis, B = 54 μT = 54 × 10^(-6) T
Step 2: Substitute the given values into the formula and solve for I:
54 × 10^(-6) = μ₀ * I * (0.03)² / (2 * ((0.03)² + (0.04)²)^(3/2))
Step 3: Simplify the equation:
54 × 10^(-6) = μ₀ * I * (0.0009) / (2 * (0.0009 + 0.0016)^(3/2))
54 × 10^(-6) = μ₀ * I * (0.0009) / (2 * (0.0025)^(3/2))
Step 4: Calculate the value of μ₀:
The permeability of free space, μ₀, is a constant value:
μ₀ = 4π × 10^(-7) T m/A
Step 5: Substitute the value of μ₀ into the equation:
54 × 10^(-6) = (4π × 10^(-7)) * I * (0.0009) / (2 * (0.0025)^(3/2))
Step 6: Simplify and solve for I:
I = (54 × 10^(-6) * 2 * (0.0025)^(3/2)) / (4π × 10^(-7) * (0.0009))
I ≈ 0.424 A
Step 7: Calculate the value of C:
The magnetic field at the center of the loop can be calculated using the same formula, by setting x = 0:
C = μ₀ * I * R² / (2 * (R² + 0²)^(3/2))
Substituting the values:
C = (4π × 10
- Radius of the circular loop, r = 3 cm
- Distance from the center of the loop to the point on the axis, x = 4 cm
- Magnetic field at the point on the axis, B = 54 μT
To find:
- The value of the magnetic field at the center of the loop, C
Explanation:
The magnetic field due to a current-carrying circular loop at a point on its axis can be calculated using the formula:
B = μ₀ * I * R² / (2 * (R² + x²)^(3/2))
Where:
- B is the magnetic field at the point on the axis
- μ₀ is the permeability of free space, which is a constant value
- I is the current flowing through the loop
- R is the radius of the loop
- x is the distance from the center of the loop to the point on the axis
Step 1: Convert the given values to SI units:
- Radius of the circular loop, r = 3 cm = 0.03 m
- Distance from the center of the loop to the point on the axis, x = 4 cm = 0.04 m
- Magnetic field at the point on the axis, B = 54 μT = 54 × 10^(-6) T
Step 2: Substitute the given values into the formula and solve for I:
54 × 10^(-6) = μ₀ * I * (0.03)² / (2 * ((0.03)² + (0.04)²)^(3/2))
Step 3: Simplify the equation:
54 × 10^(-6) = μ₀ * I * (0.0009) / (2 * (0.0009 + 0.0016)^(3/2))
54 × 10^(-6) = μ₀ * I * (0.0009) / (2 * (0.0025)^(3/2))
Step 4: Calculate the value of μ₀:
The permeability of free space, μ₀, is a constant value:
μ₀ = 4π × 10^(-7) T m/A
Step 5: Substitute the value of μ₀ into the equation:
54 × 10^(-6) = (4π × 10^(-7)) * I * (0.0009) / (2 * (0.0025)^(3/2))
Step 6: Simplify and solve for I:
I = (54 × 10^(-6) * 2 * (0.0025)^(3/2)) / (4π × 10^(-7) * (0.0009))
I ≈ 0.424 A
Step 7: Calculate the value of C:
The magnetic field at the center of the loop can be calculated using the same formula, by setting x = 0:
C = μ₀ * I * R² / (2 * (R² + 0²)^(3/2))
Substituting the values:
C = (4π × 10
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The magnetic field due to a current-carrying circular loop of radius ...
Magnetic field at any point on the axis of coil,
At the centre of coil,
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The magnetic field due to a current-carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is 54 μT. Its value at the centre of the loop is CμT. What is the value of C?Correct answer is '250'. Can you explain this answer?
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The magnetic field due to a current-carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is 54 μT. Its value at the centre of the loop is CμT. What is the value of C?Correct answer is '250'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The magnetic field due to a current-carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is 54 μT. Its value at the centre of the loop is CμT. What is the value of C?Correct answer is '250'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnetic field due to a current-carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is 54 μT. Its value at the centre of the loop is CμT. What is the value of C?Correct answer is '250'. Can you explain this answer?.
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